[HN Gopher] A guide for people who want to self-study the basics...
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       A guide for people who want to self-study the basics of computer
       science
        
       Author : tsingy
       Score  : 217 points
       Date   : 2023-06-18 13:43 UTC (9 hours ago)
        
 (HTM) web link (github.com)
 (TXT) w3m dump (github.com)
        
       | ggr2342 wrote:
       | For understanding higher math I have found this primer course
       | extremely useful:
       | 
       | Introduction to Mathematical Thinking by Keith Devlin (Stanford)
       | https://www.coursera.org/learn/mathematical-thinking
        
         | Zolomon wrote:
         | I read this book which helped me understand what it finally
         | meant to think mathematically. Highly recommended, Keith is a
         | fantastic lecturer.
        
       | totierne2 wrote:
       | I am looking for a bottle of computer science motivation for my
       | 16 year old. I do an hour a week coding with him. It is not
       | enough, he does no coding in between times. There are other
       | things he prioritises ahead of coding. (School, music, YouTube
       | videos, and chess.)
        
         | qup wrote:
         | Chess-related chatbot? Something his friends/chat room/twitch
         | can interact with, that has some kind of chess functionality.
         | 
         | Look up "aol chat coms" for inspiration from the 90s.
         | 
         | There used to be bots that played a scrambler game in AOL chat,
         | you could make a chess-related one.
        
         | Swizec wrote:
         | Maybe your son is not into coding and that's okay. This is not
         | a great profession to be in if you don't enjoy it.
        
         | gigatexal wrote:
         | Let him find his passion. Don't force him into programming.
         | There's plenty in the tech space that needs doing. And there's
         | even more in life that he can do to earn a living that's not
         | tech related.
        
           | hooverd wrote:
           | Imagine doing science, engineering, or mathematics. Might as
           | well be getting an English degree.
        
         | mywacaday wrote:
         | Pushing him to do something weekly that he doesn't sound
         | interested in at the moment will only push him away from it in
         | the longer term. Maybe try programming something that overlaps
         | with his other interests that deepens his understanding of both
         | subjects.
        
         | [deleted]
        
         | tsingy wrote:
         | Try finding something that he likes, that could be enhanced
         | with programming to start with. Mine was fantasy basketball,
         | doing it with the help of computers is so much better than by
         | hand.
        
           | Cerium wrote:
           | And keep it approachable! There is nothing wrong with writing
           | that fantasy basketball calculator as a spreadsheet.
           | 
           | Spreadsheets have many advantages that get overlooked by
           | pushing for a "real language" while jump into a programming
           | language involves learning a lot of new concepts at once.
           | 
           | For example, spreadsheets make all the memory visible at
           | once. It makes sense like a piece of paper. You also have
           | intuitive understanding of your algorithms memory
           | consumption. Computing something for N by N obviously uses
           | N^2 cells. Many problems will be solved in 2^n which will
           | mean dragging down that cell for a short while at low values
           | and suddenly a very long while.
        
         | gareve wrote:
         | create a music or YouTube bot together
        
         | LocalH wrote:
         | Then stop focusing on trying to get him to code, and focus on
         | his music, his chess, his YouTube videos ( _especially_ if he
         | has aspiration to be a content creator rather than a passive
         | consumer), and his academics. Maybe related to one of those
         | things, you could gently try to build a bridge between them and
         | coding. However, _don 't force it_. If you force it, you're
         | essentially going to be raising someone who _hates_ programming
         | because  "it's that shit my mom/dad forced me to do when I had
         | no interest in doing it, I really wanted to be developing my
         | chess game instead".
        
           | voz_ wrote:
           | This is good advice if you live in a Hollywood movie fantasy,
           | or are insanely rich. Otherwise this is bad advice.
           | 
           | A parents job is to steer their kids not into superficial
           | happiness found through whatever interested them at 16, but
           | to actual long term happiness achieved through fulfillment,
           | accomplishment, stability, and belonging.
           | 
           | If I ignored CS pushed by my father to focus on whatever
           | interested me at 16 (pot, girls, metal music, wow), I'm not
           | sure where id be, but I imagine it would be worse off.
        
             | cinntaile wrote:
             | It's neither good nor bad advice. It will depend on the
             | kid. Some will respond like you, while some will respond
             | like the commenter above you explains.
        
             | waboremo wrote:
             | I believe you interpreted their comment as a sort of let
             | them drown in hedonism moment, but from what I'm getting
             | it's really just encouraging giving your kid space to find
             | the joy themselves. You can encourage new forms or methods
             | to see if it'll stick but you still have to let them be
             | their own person. Forcing anything will just make your kid
             | resent that entirely, and for a lot of parents they don't
             | even realize this resentment of [subject/task/etc] also
             | turned into a resentment of the parent.
             | 
             | Also I think you're too pessimistic about your past
             | potential. You could have made a great musician, esports
             | pro, hell there are even some successful marijuana
             | companies now! I don't say this to stoke the flames of what
             | ifs, but instead to highlight that it wasn't exactly your
             | father's push for CS that is the only reason for your
             | success. You should absolutely take some responsibility for
             | committing and be proud of that, of course you can
             | definitely attribute your understanding of why commitment
             | is important to your father if that holds true!
             | 
             | Now that's good advice, teach your kids the importance of
             | integral foundations like commitment, don't obsess over
             | which specific field it is.
        
         | dkjaudyeqooe wrote:
         | Appeal to his music interests. This book looks pretty good and
         | uses free tools:
         | 
         | https://www.routledge.com/Introduction-to-Digital-Music-with...
        
         | password4321 wrote:
         | Lots of ideas two days ago:
         | 
         |  _Two years of teaching high school CS_
         | 
         | https://news.ycombinator.com/item?id=36355172
        
         | dybber wrote:
         | 1) Make him come up with the projects to do. Use brainstorming
         | techniques. Only help by guiding, not by telling him to do
         | specific things
         | 
         | 2) Build your similar own projects as well
         | 
         | 3) Try with electronics. For that age group I have had good
         | succes with MicroPython on ESP32's + various sensors/actuators.
         | The first thing I do is connect an LED strip with RGB LED's and
         | let them play with that.
         | 
         | 4) Find him peers with the same interest. In that age peers are
         | better partners. You can still help facilitate a bit, but the
         | best would be to find a Coding club.
        
           | lostmsu wrote:
           | > Make him come up with the projects to do. Use brainstorming
           | techniques. Only help by guiding, not by telling him to do
           | specific things
           | 
           | I found it difficult to do with a person who did not get how
           | to use control flow and can not mentally combine multiple
           | control flow constructs.
        
       | imranq wrote:
       | I had a student who was basically performing at a 6th grade math
       | level despite being in 11th grade. I told that student to go
       | through Khan Academy starting from Pre-K all the way to 12th
       | grade and don't continue unless they achieved mastery. That
       | student went from the C math student, to ultimately scoring a
       | perfect score on the SAT II Math. So I highly recommend everyone
       | start for the absolute basics, even if it feels like a blow to
       | the ego
        
       | cactusfrog wrote:
       | The CMU database course is fire
       | 
       | I want to make a non C++ workbook for that course to write an
       | s3-based relational database (for fun), but I don't have time for
       | other projects because of poor time management
        
       | teunispeters wrote:
       | As someone who could never afford to get a degree at university,
       | I love this kind of stuff!
       | 
       | I have gaps in my own knowledge, so I keep going through stuff,
       | to find what I'm missing and fill it in. Eg I'm not great on O(x)
       | calculations.
        
       | tsingy wrote:
       | Might interest some people looking to learn some Computer Science
       | basics. It's a small aggregation of openly auditable university
       | courses.
        
       | KnobbleMcKnees wrote:
       | Not sure on the prerequisites. I have absolutely no discipline
       | and still managed to get my compsci degree!
        
         | ghaff wrote:
         | That probably because you were in a degree program. Discipline
         | is definitely an issue if you just decide to complete a couple
         | dozen courses making up a curriculum from OCW or whatever. Even
         | if you take out elective stuff, especially that not connected
         | to the major, you're almost certainly talking many hundreds of
         | hours to plow through a college major.
        
           | vidyesh wrote:
           | I think the elective stuff might also be a reason to be able
           | to successfully finish the degree. University degree for many
           | comes down to studying strategically than understanding
           | everything they are studying. So the elective stuff might be
           | considered a break from other stuff, which means the brain
           | does get time to take a break from a certain topic to retain
           | that information while you study something else.
           | 
           | Self-study is a road with very little guidance to understand
           | which part is more important to study, and which just needs
           | to be understood so the pressure to make sure one knows
           | everything makes it difficult to progress at a consistent
           | pace.
        
             | ghaff wrote:
             | >Self-study is a road with very little guidance to
             | understand which part is more important to study, and which
             | just needs to be understood so the pressure to make sure
             | one knows everything makes it difficult to progress at a
             | consistent pace.
             | 
             | Part of it is that there's also the question of what your
             | goal is.
             | 
             | If you down an MIT CS+EE degree curriculum in OCW, you're
             | actually not going to have a huge amount of programming
             | except as a byproduct. If your actual objective is to learn
             | front-end development, I'm guessing you won't actually have
             | learned that by the time you're done. I'm guessing most
             | people looking for a self-directed CS bootcamp don't
             | actually want a "CS" bootcamp.
        
           | KnobbleMcKnees wrote:
           | Jokes aside, I agree. University programs do/can provide an
           | almost overbearing amount of structure, and that worked well
           | for me.
        
       | hcks wrote:
       | That's just the usual memes. Is this about << computer science >>
       | ? Then why isn't there anything logic, algorithms, Turing
       | machines, etc.. Is this << dev >>? Then what's the point of
       | discrete maths?
        
         | ke88y wrote:
         | _> Is this << dev >>? Then what's the point of discrete maths?_
         | 
         | You can probably retire on a 6% coupon if you save a lot, but
         | you'll have a much more comfortable retirement if you can clip
         | a 15% coupon on those same savings.
         | 
         | Discrete Mathematics is usually some mish-mash of formal logic,
         | induction, combinatorics, number theory, and baby probability.
         | You can get away without knowing these things, but studying
         | them doesn't take very long (14 weeks, part time?!) and pays a
         | very handsome dividend. A foundation in this sort of knowledge,
         | and practice operationalizing it, is often the difference
         | between $60K/yr and $100K+/yr for junior developers. The size
         | of the dividend payment generally increases as one's career
         | progresses, assuming you stay on the IC track.
         | 
         | Induction and formal logic are useful for reasoning about
         | programs that contain loops. Often you can get away with
         | intuitive understanding, and many people program for years
         | before encountering problems where formal and structured
         | reasoning becomes necessary (myself included!). But most well-
         | paid developers will encounter a problem or two each year where
         | reasoning about non-trivial loops is required and where the
         | basics of induction and formal logic are tremendously helpful.
         | 
         | Exposure to basic thinking techniques in combinatorics is
         | essential for reasoning even informally about time and resource
         | complexity. Writing code that relies on non-trivial time and
         | resource complexity analyses is occasionally necessary in most
         | well-paying developer positions.
         | 
         | The very basics of number theory is useful for understanding,
         | conceptually, how cryptography works. This isn't essential for
         | most dev positions. But it is helpful knowledge.
         | 
         | Baby probability is increasingly required knowledge for many
         | dev positions, and not just because of the explosion of
         | AI/ML/DS.
         | 
         | Again, you don't need this material often. You can probably go
         | an entire career avoiding the brutal pain of spending 14 weeks,
         | 1-2 hours per work day, studying simple mathematics. But the
         | ability to pull these skills out when they're needed is the
         | difference between commodity "keep him around if we have
         | billable hours" bootcamp labor and in-demand "smart and we
         | really need to keep him around and eventually promote him to
         | principal" labor.
        
         | kandel wrote:
         | year 1 CS in my university is
         | 
         | :intro to CS (simple JAVA and simple coding) :linear algebra 1
         | :introduction to logic (simple set theory(though the course got
         | comparatively deep and proved induction as well as defined
         | relations rather throughouly. most students failed.) :Digital
         | systems (basic digital logic)
         | 
         | semester 2 is: :data structures :linear algebra 2 :infitisimal
         | math 1 :practical course on usages of math :combinatorics\basic
         | discrete math (No generator functions or the like. Basic
         | counting, basic graph theory, basic discrete probability)
         | 
         | This is for a university that has a technical approach to CS.
         | It's not considered very mathematical, so view it as a sign
         | that calc1/2 and linear algebra 1/2 is needed. they are fun
         | courses! Go learn the math courses with the mathematicians if
         | you've felt a connection to math, there is a definite change in
         | the feelings of the class. It's the "same" material but in one
         | class you will think like a mathematician and in the other like
         | an engineer.
        
       | satvikpendem wrote:
       | I've found Teach Yourself CS a better resource, albeit more
       | advanced: https://teachyourselfcs.com
        
       | [deleted]
        
       | hahhahanananana wrote:
       | > High School Mathematics
       | 
       | Whenever I try to catch up with maths (in Khan Academy and
       | elsewhere), I always end up in an awkward state where I keep
       | recursively researching less and less advanced subjects because
       | of gaps of various sizes in my fundamental knowledge. It's
       | incredibly demotivating.
        
         | vector_spaces wrote:
         | I guess first consider that you might have math trauma -- read
         | about it, own it (if it applies, of course), and recognize what
         | it feels like when it rears its head. Lots of people -- mainly
         | in the US, but it's a thing in other countries too -- were
         | taught math in a pretty shitty way, often by people who don't
         | want to be teaching it in the first place because they
         | themselves have math trauma.
         | 
         | Then build up fluency in the basic manipulations: do lots and
         | lots and lots of exercises until those manipulations become
         | second nature. You might need to start with fractions[2], and
         | that's fine. One of the nice things about math at the
         | elementary level is that you nearly always are guaranteed to
         | get better with practice. This absolutely isn't the case for
         | proof-based math, where you really need to be intentional about
         | truly digesting the material and thinking careful about the
         | ideas. But if you're shaky on absolute fundamentals, you can
         | get incredibly far with grinding.
         | 
         | At some point you'll need to engage with the ideas, but I think
         | that's easier once you've built up some pattern recognition.
         | But others will (surely) disagree
         | 
         | [1] https://www.edweek.org/teaching-learning/opinion-how-to-
         | help...
         | 
         | [2] https://www.edweek.org/teaching-learning/fraction-phobia-
         | the...
        
         | OwlGoesHoot wrote:
         | It would probably be helpful to start at a level above where
         | you left off and look up specific gaps in your knowledge as you
         | find them. It's always good to come to a topic with the
         | understanding of every previous topic, but often those deeper
         | understandings come from moving into more advanced subjects
         | anyway. It might be more slow and frustrating at times, but it
         | will give you a better understanding of where your specific
         | gaps in knowledge actually lie and you'll be able to address
         | them as you go.
        
         | jayro wrote:
         | At Math Academy, we've created a sequence of math courses
         | called Mathematical Foundations I, II, & III that cover
         | everything from 5th Grade Math up through Calculus I & II and
         | will allow anyone to get up to speed on the skills required for
         | university-level mathematics in the most efficient way
         | possible. Our adaptive diagnostic exams will create a custom
         | fit course no matter where you are mathematically and our
         | algorithms will continually adapt to your individual strengths,
         | weaknesses and learning curve.
         | 
         | https://mathacademy.com/courses/mathematical-foundations-i
         | https://mathacademy.com/courses/mathematical-foundations-ii
         | https://mathacademy.com/courses/mathematical-foundations-iii
         | 
         | In addition, we have courses on Linear Algebra and Mathematics
         | for Machine Learning, with more coming soon:
         | 
         | https://mathacademy.com/courses/linear-algebra
         | https://mathacademy.com/courses/mathematics-for-machine-lear...
         | 
         | The system is mastery based, lightly gamified, and completely
         | automated. Our algorithms intelligently apply spaced-repetition
         | to a hierarchical knowledge graph of over 3,000 mathematical
         | concepts to make it substantially more efficient than a
         | traditional course (typically on the order of 4X or more).
         | 
         | I'm a founder and would be happy to answer any questions.
        
         | bovem wrote:
         | It might not be the same for you. But this is what I enjoy when
         | I study anything. Filling up the gaps in my knowledge and
         | learning about new ways to think or understand about a concept.
         | Maybe you shouldn't dive so deep into the concepts. Just write
         | all the topics/concepts you didn't understand while learning
         | something and watch one video about each of them.
        
         | danielvaughn wrote:
         | Weirdly enough, mathematics is a very emotional subject for me.
         | I never understood how it was taught in school, and had serious
         | difficulty understanding it. As a result I just ignored it,
         | believing that I didn't have the right brain for it.
         | 
         | Even though I taught myself how to code, I never went back and
         | learned math, so my level of knowledge is at a basic high
         | school level. It can be embarrassing at times, and every now
         | and then I think about trying to learn it.
        
           | wonderingwhale wrote:
           | I honestly think this is one of the bigger problems with
           | people who "can't do math", probably most people can learn
           | quite a bit of (at least basic) mathematics. But oftentimes
           | when you did not understand the subject well previously, like
           | in high school because of different interests at the time or
           | a bad teacher or something. And then because of this whenever
           | you see an equation or hear the word 'mathematics' you just
           | shut off your brain. I know some people who can understand me
           | when I explain some physics or mathematics concept without
           | explicit mathematics, but they would be scared off at the
           | first equation.
        
         | vidyesh wrote:
         | Too many false starts too lead to doing the same fundamentals
         | all over again, making one feels like they are not progressing
         | at all.
         | 
         | I remember reading somewhere, do the implementation of it along
         | side fundamentals. The reason you are studying fundamentals to
         | progress ahead, do that course along side too. This helps one
         | grasp the fundamentals quickly and more importantly to know
         | which fundamentals you really need than to try to do everything
         | and forget aspects of it later.
         | 
         | That being said, I am yet to implement that concept and get
         | over false starts
        
         | ke88y wrote:
         | Paradoxically, self-teaching is most difficult at the "101" and
         | "pre-101" level. Once you have the basics, self-teaching
         | becomes much easier.
         | 
         | Teaching yourself Calculus I and Calculus II after obtaining
         | High School mathematical literacy is not too bad. Teaching
         | yourself Differential Equations or even Functional Analysis
         | after obtaining the pre-reqs is actually quite easy. But
         | teaching yourself high school or especially middle school
         | mathematics requires a TON of dedication.
         | 
         | It's not impossible, of course, but "The Basics" are where you
         | _really_ benefit from the help of a professional educator.
         | 
         | For this reason, I recommend eschewing self-directed resources
         | and enrolling in an "Applied Math" or "College Algebra" course
         | at your local community college. These courses are basically
         | "high school mathematics for people who never learned or forgot
         | high school mathematics". Depending on where you live, the
         | "College Algebra" course at your local Community College is
         | probably very cheap or free and available as an evening and/or
         | online course. You usually do not need to enroll in a degree
         | program to take the course.
         | 
         | Once you make it through "College Algebra" you can return to
         | self-directed learning.
         | 
         | Community Colleges are a vastly under-utilized resource,
         | particularly for these "very fundamental knowledge gaps" where
         | self-directed learning is much more difficult.
        
         | yt-sdb wrote:
         | Maybe 5 years ago, I was in a similar place. I had a
         | particularly embarrassing moment at work when it clicked that I
         | just... didn't know the basics. I was, to use an overused term,
         | "mathematically immature".
         | 
         | So I made a commitment: I decided I would work through Khan
         | Academy math for 1-hour a day for 1 year. I started with pre-K
         | [1] (specifically counting) and watched every video and did
         | every single exercise in order. I focused on mastery. I didn't
         | rush myself, and I did not continue until I felt completely
         | confident in the material. I just did this for a year. I think
         | I go through roughly algebra 2. In my mind, it is critical to
         | combine explicit knowledge (watch videos) with tactic knowledge
         | [2] (do exercises). For example, you need to understand what a
         | logarithm is conceptually but you also just need to do problems
         | to get a feel for it. So this is fundamentally different than
         | learning-by-grazing or just reading a book.
         | 
         | I could go on and on, but let me just say that it changed my
         | relationship to math in a deep way.
         | 
         | [1] https://www.khanacademy.org/math/k-8-grades [2]
         | https://commoncog.com/tacit-knowledge-is-a-real-thing/
        
           | xwowsersx wrote:
           | What did you do after you completed the K-8?
        
             | yt-sdb wrote:
             | I worked from the top of this page [1] downwards and ended
             | after algebra 2.
             | 
             | [1] https://www.khanacademy.org/math
        
           | noSyncCloud wrote:
           | This is really inspiring, thanks for sharing. I should do
           | likewise. I wound up dropping out of school (had kids too
           | early, don't ask), which was... not a good decision. I do
           | work as a developer but I need more domain knowledge in
           | mathematics. Never too late to start, I guess.
        
           | gareve wrote:
           | if you would have to do it again, would you change something
           | on your methodology? I assume there were some unnecessary
           | time sinks here & there
        
             | gpt5 wrote:
             | If you, or someone else is seriously considering learning
             | math from the basic at a high level, I'd recommend picking
             | up "art of problem solving, pre-algebra" book, and walking
             | up from there.
             | 
             | These sets of books are universally considered to be among
             | the best math education resources by mathematicians and
             | others, and they start from the very basic (such as the
             | number line and basic operations), but without the need of
             | practicing elementary school material like counting.
        
               | jacksnipe wrote:
               | I think the TAOPS curriculum would be incredibly
               | challenging for somebody who has actively incorrect
               | intuitions about math.
        
             | yt-sdb wrote:
             | I don't think so. My problem was that I had a weak grasp of
             | many basics concepts, and more critically I did not know in
             | which areas I was weak. So while it's easy ex post to say
             | "I could skip such and such section", it would have been
             | impossible to make this judgment ex ante.
             | 
             | And in fact, I think a failure mode many people make is
             | trying to predict which things they already know and then
             | skipping those. This allows for blind spots to persist.
             | 
             | I suppose the one way to skip things correctly would be to
             | have a coach. But that comes at a new cost ($), but maybe
             | that works for some people.
        
               | hawk_ wrote:
               | I have been seeing more and more usage of 'ex post' and
               | 'ex ante' lately. What do they convey that isn't conveyed
               | by 'after' and 'before'?
        
               | yt-sdb wrote:
               | "Before" and "after" are generic terms. A car might stop
               | before the crosswalk (space). You might eat dinner after
               | work (time). But "ex ante" and "ex post" specify a
               | relationship to an (random) event or to specific
               | information. For example, a data scientist might compute
               | a quantity "ex ante". This means that the quantity was
               | estimated using only forecast data. No historical data
               | was used. It would not make sense, however, to say that a
               | car stops ex ante the crosswalk.
               | 
               | I could have easily said "afterwards" and "beforehand",
               | but I like "ex post" and "ex ante" when referring to
               | before/after having access to specific information.
        
               | hawk_ wrote:
               | Got it. I will try to leverage the synergies between
               | Latin and English ex post.
        
               | timidiceball wrote:
               | it conveys that you know what ex post and ex ante mean
        
               | jhardy54 wrote:
               | Or, quite often, conveys that you don't know what they
               | mean.
        
           | status200 wrote:
           | This is inline with a Zen practice called "beginner's mind",
           | and is so useful in many areas, thank you for this
           | inspiration.
        
         | randmeerkat wrote:
         | > Whenever I try to catch up with maths (in Khan Academy and
         | elsewhere), I always end up in an awkward state where I keep
         | recursively researching less and less advanced subjects because
         | of gaps of various sizes in my fundamental knowledge. It's
         | incredibly demotivating.
         | 
         | Try this course: https://www.edx.org/course/college-algebra-
         | and-problem-solvi...
         | 
         | It uses the ALEKS system which identifies your weak points and
         | brings you up to speed. Take notes during the process so you
         | have something to reference in the future and won't forget what
         | you learned.
         | 
         | After you knock out the algebra course you'll be ready for the
         | precalculus course: https://www.edx.org/course/precalculus
         | 
         | The ALEKS system in the Precalculus course will also remediate
         | anything you forgot from the Algebra course.
         | 
         | Hopefully this will help give you the confidence to go after
         | more advanced maths once you finish both courses. Be kind to
         | yourself, math, like anything, is a skill, it takes time and
         | practice.
        
         | satvikpendem wrote:
         | Why not start from the beginning, ie pre-K on up, as the other
         | commenter mentioned? I've done something similar for teaching
         | myself web development (since it's not taught often in CS
         | degree programs), starting from bare HTML, adding CSS, adding
         | Javascript, adding TypeScript, adding React, and so on. Now I
         | have a good foundation from which to build anything I want. So
         | too with mathematics or really any subject.
        
         | glass-z13 wrote:
         | Same for me, let me know if you find the solution! I think it's
         | extremely hard to get into this kind of stuff when you
         | basically have to start from 0 meanwhile everyone else has a
         | better foundation than you
        
         | Cerium wrote:
         | Have you seen "An Infinitely Large Napkin"? I saw it posted
         | here a couple years ago. It is Evan Chen's project "aimed at
         | making higher math accessible to high school students."
         | 
         | https://web.evanchen.cc/napkin.html
        
         | tsingy wrote:
         | The book that made things click for me was Maths: A Student's
         | Survival Guide by Jenny Olive. Give it a shot, use a calculator
         | for everything. IMO in the age of computers let computers do
         | the calculations and just learn to have intuitions.
        
           | ghaff wrote:
           | I'd have to be convinced that you can develop those
           | intuitions without basic arithmetic. Mind you, I'm not saying
           | spend a lot of time mastering long division or whatever. (I'd
           | probably have to look up the technique myself.) But I think
           | some level of numeric fluency is probably necessary.
        
             | 2devnull wrote:
             | "I'd probably have to look up the technique myself."
             | 
             | No offense but I am pretty sure that was the point. If it's
             | math you forget, it's not math worth learning. Learn what
             | you want or need to know. The rest is dross.
        
         | poulsbohemian wrote:
         | My 13 year old is a very good student, currently taking high
         | school math classes while in middle school... one of the things
         | that the public school system hasn't figured out is how to make
         | any of it relevant. So sure, she's brilliant and flies through
         | the material, but she'd be the first to tell you it's just
         | puzzles, it has no actual meaning to her. I was the opposite -
         | because it had no meaning to me, I couldn't understand it and
         | was a terrible math student. But, once I could view it through
         | the lens of computer science, suddenly it had meaning and I did
         | fine.
         | 
         | My oldest daughter was a terrible student. But she would say to
         | me "If they taught history class the way you explain historical
         | events around the dinner table, I would have been a lot more
         | interested in studying."
         | 
         | So point being - it's probably not you, a lot of it really is
         | the way we approach k-12 education. In hindsight, I'm not sure
         | college is any better and may be worse what with the approach
         | of hazing and weeding out.
        
           | gnicholas wrote:
           | The Khanmigo chatbot that KA is rolling out supposedly helps
           | with this problem of relevance.
        
         | ranieuwe wrote:
         | I have the same problem and have still not found a workable
         | solution.
         | 
         | Only one there seems to be is to basically rerun 12 years of
         | math, which is really unpleasant because I know 80% of the work
         | making it unrewarding and slow. I don't know what I don't know
         | that is super demotivating, indeed.
        
         | xwowsersx wrote:
         | Another resource I wanted to mention here is OpenStax.
         | Specifically, their Prealgebra book:
         | https://openstax.org/details/books/prealgebra-2e it's a fully
         | online-native book format with exercises, etc.
        
         | EGreg wrote:
         | For what it's worth, if you want to go bottom-up and give
         | yourself a super-solid foundation, go through the videos I
         | recorded several years ago specifically for this purpose. They
         | are for children as well as adults:
         | https://www.youtube.com/@thinkingmathematically
         | 
         | Please let me know if they were helpful!
        
       | EGreg wrote:
       | Is this like Poor Richard's Almanac?
        
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